Design of 4UM-120D Electric Leafy Vegetable Harvester Cutter Height off the Ground Automatic Control System Based on Incremental PID

Round 1

Reviewer 1 Report

In this study, authors developed the 4UM-120D electric leafy vegetable harvester, and designed an automatic control system for the height of the cutter from the ground, which kept the height of the cutter from the ground within ±2% of the set value. They reported that the purpose was to increase the working quality of the leafy vegetable harvester and decrease the working intensity of the operators. The most important key sentence of this study is "The quality of the leafy vegetable harvest will be impacted if the height of the ridge surface (boundary surface) changes, which would result in varied leafy vegetable stubble heights". With this proposed system, the cutting height can be adjusted by PID control for different ground conditions. The authors presented a work with a clear methodology. I think that the work described in the manuscript is interesting. In general the work is well structured. Figures and tables are descriptive and sufficient. References are sufficient and belong to the last 10 years. However, I believe that the some important details in the study need to be given before the manuscript can be published. I have listed my comments and suggestions below.

 

Comments and Suggestions:

 

1.      I think the resolution of some images should be increased. I also suggest that the font of the texts in the flowcharts should be the same as the main text (See Fig.5, 6..).

 

2.      Any faults and warnings indicated by the system? Limitations of this study? I think it would be better if an explanation could be added to the article about these issues.

 

3.      Battery capacity was not given in Table 1.

 

4.      I think the work is very important. Thank you for contributing to the scientific literature on the subject.

Minor editing of English language required. I recommend making the final reading and splitting the long sentences into shorter sentences that are more understandable.

Author Response

Response to Reviewer 1 Comments

Point 1: I think the resolution of some images should be increased. I also suggest that the font of the texts in the flowcharts should be the same as the main text (See Fig.5, 6..).

 

Response 1: Thank you for your valuable suggestions. I apologize that some of the images in this manuscript are too low resolution. I also apologize that the font of the texts in the flowcharts are not the same as the main text. The modified figures are shown in Figure 1(a) to Figure 8(a).

Figure 1(a). SLIDE FW leafy vegetable harvester.

Figure 2(a). 4UGS2 type double row sweet potato harvester.

Figure 3(a). Sketch of the structure of the 4UM-120D electric leafy vegetable harvester.

Figure 4(a). Automatic adjustment system of cutter height from the ground.

Figure 5(a). Flow chart of the automatic adjustment program of the cutter height off the ground.

Figure 6(a). Model of cutter height adjustment system from the ground.

Figure 7(a). Position-based PID control schematic.

Figure 8(a). Incremental PID-based model for automatic control system of cutter height off the ground.

 

Point 2: Any faults and warnings indicated by the system? Limitations of this study? I think it would be better if an explanation could be added to the article about these issues.

 

Response 2: Thank you for your valuable suggestions. If the left limit switch of the automatic adjustment system of cutter height from the ground was on, the system would issue a warning and the stepper motor would stop rotating to prevent the slide block from hitting the stepper motor and causing motor damage. If the right limit switch of the automatic adjustment system of cutter height from the ground was on, the system would also issue a warning and the stepper motor would stop rotating to prevent the cutter from being damaged by touching the ground due to the low height of the cutter from the ground. As the automatic control system for the height of the cutter off the ground was a semi-closed loop system, i.e. sampled from the motor, there must be an error in accuracy, and it was an order of magnitude difference compared to a closed loop system, but at this stage the "yes" and "no" problems were first ensured and the rest was left for later. However, there was a need to acknowledge the errors and recognize the problems involved, as well as providing a basis for further research on the subject to improve accuracy.

 

Point 3: Battery capacity was not given in Table 1.

 

Response 3: Thank you for your valuable suggestions. I apologize that the battery capacity is not given in Table 1. The battery capacity is 50Ah. The modified table is shown in Table 1(a).

 

Table 1(a) 4UM-120D electric leafy vegetable harvester structural parameters and technical parameters

Parameters	Values
Whole machine size(length×width×height)/(mm×mm×mm)	2180×1500×1200
Battery capacity/Ah Working width/mm Cutter height adjustment range/mm Conveyor belt width/mm Conveyor belt installation inclination/° Wheelbase/mm Wheel radius/mm Minimum ground clearance/mm Productivity/	50 1200 0~100 1200 30 550 175 70 0.04~0.08

 

Point 4: I think the work is very important. Thank you for contributing to the scientific literature on the subject.

 

Response 4: Thank you very much for taking time out of your busy schedule to make invaluable suggestions to me. Thank you for your recognition and support of our work. "Agriculture" magazine is a very good journal. It is my honor to have my manuscript accepted by "Agriculture", and I also hope that my manuscript can be accepted by it. Please also kindly contact me if you have any suggestions during the review of my manuscript. Thanks again for the suggestion you gave me during your busy schedule.

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

 

Agriculture – REVIEW

 

Design of 4UM-120D electric leafy vegetable harvester cutter height off the ground automatic control system based on incremental PID

 

Overview:

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The paper presents a leafy green harvesting machine, specifically a system which keeps track of the height above the ground of the machine’s cutter. A PID (incremental) regulator system has been designed to manipulate the cutter height which is actuated by a stepper motor via a ball screw mechanism.

This system has been tested in both simulation and field testing. The simulation is conducted using an elaborate stepper motor model and the model of its driver.

The simulation and field testing give similar results from what it has been concluded that the system operates as intended.

 

Comments based on the text and figures:

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113 – 119:

The sentence describing the contents of the paper is rather long and very hard to follow. Please, consider rephrasing in multiple simple sentences.

 

Table 1:

There is a problem with the data alignment – it starts with the battery capacity. The data itself seems to be in order.

 

174 and 188:

In the text it is stated that the motor stops rotating when the measured height is within ±2% of the set height. Can you explain at which height is the control algorithm actually aiming: does it stop as soon as the measured height is within this range, or attempts to set the height value exactly (to the set value)?

 

Figure 5:

The diagram represents a control algorithm. Its purpose is to continually monitor and adjust the height of the cutter. The algorithm has a start, which can be understood as the state of the machine right after reset. The algorithm doesn’t have any end which is acceptable, since it should continuously adjust the height of the cutter. The problem is that the state at the bottom seems to be a dead end. The algorithm does not continue anywhere from that point. One would expect that the algorithm contains an endless loop which provides constant cutter adjustment, however in the algorithm presented here this is not the case. Please correct this, or give an explanation why is the algorithm drawn like this.

 

Formula (7):

It would be a good idea to replace the indices with Chinese characters with some more convenient (international) letters.

 

254 – 266: 2.4.2 Analysis of incremental PID control strategy

This paragraph is very hard to follow. It would be a good idea to back the explanation with appropriate formulae or a figure. The formulation is clumsy to say the least. The language is grammatically more or less correct, but the point of the incremental strategy is impossible to understand. Since the incremental PID is the main point of the paper, this issue must be addressed.

 

267 – 281: 2.4.3 Difference between position and incremental PID control

Due to the problems with the previous section, it’s very hard to conclude what the authors are actually referring to in this section. For example, I guess that by “no need to accumulate incremental PID” they mean that there is no need to calculate the value of the integral contributioon, but this should be clearly stated.

A good explanation in the previous section would make a huge impact on this section. However, some corrections would be necessary to this section too, depending on the changes made to the previous section.

 

Figure 6

The figure should have a higher resolution, the small text is hard (or impossible) to read.

 

Figure 8

The figure should have a higher resolution, the small text is hard (or impossible) to read.

 

 

Other Issues not Tied to any Specific Point in the Text

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1.

At the beginning of the paper a photoelectric sensor is mentioned as part of the system (line 180). However, this sensor is not mentioned in the description of the control system, neither in simulation, nor in hardware? Does it mean that is was not implemented? This should be clearly stated in the paper that it was not actually used, its action is only assumed.

 

2.

In accordance with the previous comment, all simulations and measurements were conducted by actually changing the set cutter level in time and observing the control system’s response to this. Please, explain this in the paper, or correct me if I’m wrong in my observation.

 

3.

Crossing the ditch: a narrow strip of lower ground was in front of the harvester which led the sensor to believe that the cutter was too high, therefore it should be lowered.

Another interpretation: the wheels entered the ditch which lowered the cutter and it should be lifted.

As I understand, the first case is what you intended. Please clarify this in the paper.

 

4.

In both simulation and experiment it should be clearly stated what the reaction should be, and what actually happened. Which direction of movement is represented as positive, which one as negative? Did the system actually lower or lift the cutter? Please be explicit about these elements in the presentation of the results.

 

5.

In Figure 9, d) and e) the reference (set values) and actual outputs never get equal (the set value is never reached?). Why is that? Please comment on this.

 

6.

Figure 10 e) and Figure 14 should show the exact same thing. Why is in Figure 14 (the real measurement) only one motion (in the negative direction), and not two motions in both directions as in Figure 10 e)? If I understand it correctly, the upward slope came about, the cutter should go up, then down (when the whole machine is driven on the slope). In that sense, why is there only the downward motion in Figure 14 (if I’m not mistaken)?

 

7.

I’m having a hard time finding the connection between the suggested model (Figure 6) and the given equations (1 to 7). Equations (1) – (5) seem correct to me. (7) is simple enough to understand and also seems correct. However, it is not the case with equation (6), where does it come from? It might be a good idea to remove from the paper all the equations which are not used in any meaningful way. Please comment on this.

 

8.

You state your assumptions about the model (line 203):

1) the effect of stator current on the motor was not taken into account

Please explain what you mean by that. The torque of the stepper depends on the stator current (Ia and Ib) and it seems to me that this has been taken into account (by equation 4). You also have a current PID in the automatic control system (Figure 8), which means that stator current is an important part of the model and control system, otherwise it wouldn’t make sense? Please comment on that.

The other assumptions (2 – 4) seem to be in order to me.

The English text in this paper is mostly grammatically correct with practically no spelling errors. However, the style can be significantly improved. There are many unnecessary repetitions of whole sentences which are sometimes hard to tolerate. Many parts of the text lack clarity. It would mean a lot to break up long sentences to multiple short ones. I pointed out in my comments the parts I consider particularly problematic.

Author Response

Response to Reviewer 2 Comments

Point 1: 113 – 119: The sentence describing the contents of the paper is rather long and very hard to follow. Please, consider rephrasing in multiple simple sentences.

 

Response 1: Thank you for your valuable suggestion. I apologize that the sentence describing the contents of the paper is rather long and very hard to follow. The revised contents are shown below.

This study will use the 4UM-120D electric leafy vegetable harvester as the research object and create an automatic control system for the height of the cutter off the ground so that the height of the cutter off the ground is always within ±2% of the set value. Firstly, the composition and control principle of the automatic control system for the height of the cutter off the ground are described. Then, the electrical equation and mechanical equation mathematical model of the two-phase hybrid stepper motor are established in MATLAB. The principle and difference between the position PID and the incremental PID control strategy are analyzed. The incremental PID is used to establish the control strategy of the harvester cutter height off the ground. The automatic control system of the harvester cutter height off the ground under the corresponding control strategy is built. Finally, to conduct simulation testing and field tests, MATLAB/Simulink is utilized to model various real-world operating circumstances. With the steady-state transition time as the evaluation index, the stability, accuracy, and rapidity of the automatic control system of cutter height off the ground under the incremental PID control strategy are analyzed.

 

Point 2: Table 1: There is a problem with the data alignment – it starts with the battery capacity. The data itself seems to be in order.

 

Response 2: Thank you for your valuable suggestion. The modified Table 1 is shown in Table 1(a).

 

Table 1(a) 4UM-120D electric leafy vegetable harvester structural parameters and technical parameters

Parameters	Values
Whole machine size(length×width×height)/(mm×mm×mm)	2180×1500×1200
Battery capacity/Ah Working width/mm Cutter height adjustment range/mm Conveyor belt width/mm Conveyor belt installation inclination/° Wheelbase/mm Wheel radius/mm Minimum ground clearance/mm Productivity//h	50 1200 0~100 1200 30 550 175 70 0.04~0.08

 

Point 3: 174 and 188: In the text it is stated that the motor stops rotating when the measured height is within ±2% of the set height. Can you explain at which height is the control algorithm actually aiming: does it stop as soon as the measured height is within this range, or attempts to set the height value exactly (to the set value)?

 

Response 3: Thank you very much for taking time out of your busy schedule to make invaluable suggestions to me. The actual target height of the control algorithm is 0.98a~1.02a (a indicates stubble height of leafy vegetables). The stepper motor stops rotating as soon as the measured height is within this range.

 

Point 4: Figure 5: The diagram represents a control algorithm. Its purpose is to continually monitor and adjust the height of the cutter. The algorithm has a start, which can be understood as the state of the machine right after reset. The algorithm doesn’t have any end which is acceptable, since it should continuously adjust the height of the cutter. The problem is that the state at the bottom seems to be a dead end. The algorithm does not continue anywhere from that point. One would expect that the algorithm contains an endless loop which provides constant cutter adjustment, however in the algorithm presented here this is not the case. Please correct this, or give an explanation why is the algorithm drawn like this.

 

Response 4: Thank you very much for taking time out of your busy schedule to make invaluable suggestions to me. I apologize that the algorithm doesn’t have any end which is acceptable. The modified flow chart of the automatic adjustment program of the cutter height off the ground is shown in Figure 5(a).

Figure 5(a). Flow chart of the automatic adjustment program of the cutter height off the ground.

 

Point 5: Formula (7): It would be a good idea to replace the indices with Chinese characters with some more convenient (international) letters.

 

Response 5: Thank you for your valuable suggestion. The modified Formula (7) is shown in Formula (7(a)).

（7(a)）

 

Point 6: 254 – 266: 2.4.2 Analysis of incremental PID control strategy

This paragraph is very hard to follow. It would be a good idea to back the explanation with appropriate formulae or a figure. The formulation is clumsy to say the least. The language is grammatically more or less correct, but the point of the incremental strategy is impossible to understand. Since the incremental PID is the main point of the paper, this issue must be addressed.

 

Response 6: Thank you for your valuable suggestion. The revised contents are shown below.

2.4.1. Analysis of position PID control strategy

The position error of a stepper motor position PID control was calculated as the difference between the set value of the motor rotation angle and the actual rotation angle. This position error was then multiplied by the proportional, integral, and differential coefficients, and the three were added to create the control quantity. The control quantity was then applied to the stepper motor to cause it to change its rotation angle to conform to the set value. Figure 7 depicted the operation of position PID control. The transfer function of a positional PID controller was shown in equation (8). Assuming that  was the output value of the controller at the kth sampling moment, the discrete positional PID was calculated as shown in equation (9).

Figure 7. Position-based PID control schematic.

（8）

                                                                    

（9）

Where, - The transfer function of a positional PID controller; - Output of the controller; - Input of the controller; - Proportional coefficient; - Integral coefficient; - Differential coefficient; - The output value of the controller at the kth sampling moment.

2.4.2. Analysis of incremental PID control strategy

Incremental PID control of the stepper motor was to make a difference between the set value of the motor rotation angle and the actual rotation angle to form the position error e(k), the position error e(k-1) of the previous generation, and the position error e(k-2) of the previous two generations, and then make a difference between e(k) and e(k-1), and then multiply by the proportional coefficient. e(k) was multiplied by the integral coefficient, and the final differential coefficient was multiplied by (e(k)-2e(k-1)+e(k-2)). The stepper motor's rotation angle was adjusted by the control quantity, which was the total of the three, to bring it into compliance with the predetermined value. Incremental PID control was to take the increment of position PID control. The difference between the positions of the two adjacent sampling periods was the output of the control system at this time, and the control amount was the increment, which meant increasing the control amount based on the previous control amount (negative value meant reducing the control amount). The incremental PID control was calculated as shown in equation (10).

（10）

 

Point 7: 267 – 281: 2.4.3 Difference between position and incremental PID control

Due to the problems with the previous section, it’s very hard to conclude what the authors are actually referring to in this section. For example, I guess that by “no need to accumulate incremental PID” they mean that there is no need to calculate the value of the integral contributioon, but this should be clearly stated.

A good explanation in the previous section would make a huge impact on this section. However, some corrections would be necessary to this section too, depending on the changes made to the previous section.

 

Response 7: Thank you for your valuable suggestion. The revised contents are shown below.

2.4.3. Difference between position and incremental PID control

(1) Incremental PID control optimized the accumulation calculation so that the control increment no longer needed to accumulate the previous values several times, but only needed to process the most recent 3 times values, further reducing errors. It was simple to manufacture significant accumulation errors because the position PID control was tied to the error accumulation value.

(2) Incremental PID control optimized the output, and in order to ensure that the actual output had a minimal impact on the variability of the system, only the control increments were output here, making the impact of faults minimal, i.e. the occurrence of a fault with only minor problems did not seriously affect the system process. The output of the position PID control was in perfect agreement with the output of the controlled item, which significantly affected the system.

In conclusion, incremental PID control optimized the accumulation calculation so that the control increment no longer needed to accumulate the previous values several times, but only needed to process the most recent 3 times values, further reducing errors. Incremental PID control also optimized the output, and in order to ensure that the actual output had a minimal impact on the variability of the system, only the control increments were output here, making the impact of faults minimal, i.e. the occurrence of a fault with only minor problems did not seriously affect the system process. Hence, incremental PID was used in the automatic adjustment control technique for cutter height above the ground.

 

Point 8: Figure 6

The figure should have a higher resolution, the small text is hard (or impossible) to read.

 

Response 8: Thank you for your valuable suggestion. The modified Figure 6 is shown in Figure 6(a).

Figure 6(a). Model of cutter height adjustment system from the ground.

 

Point 9: Figure 8

The figure should have a higher resolution, the small text is hard (or impossible) to read.

 

Response 9: Thank you for your valuable suggestion. The modified Figure 8 is shown in Figure 8(a).

Figure 8(a). Incremental PID-based model for automatic control system of cutter height off the ground.

 

Point 10: At the beginning of the paper a photoelectric sensor is mentioned as part of the system (line 180). However, this sensor is not mentioned in the description of the control system, neither in simulation, nor in hardware? Does it mean that is was not implemented? This should be clearly stated in the paper that it was not actually used, its action is only assumed.

 

Response 10: Thank you for your valuable suggestion. I apologize that the photoelectric sensor is not mentioned in the description of the control system. There is a practical use for the photoelectric sensor, which serves to measure the height of the cutter above the ground in real time. The revised contents are shown below.

Based on the invented 4UM-120D electric leafy vegetable harvester, the automatic control system of cutter height from the ground was made up of a touch screen, a photoelectric sensor, PLC, stepper motor and its driver, ball screw device, proximity switch, etc., as shown in Figure 4(a).

Figure 4(a). Automatic adjustment system of cutter height from the ground.

 

Point 11: In accordance with the previous comment, all simulations and measurements were conducted by actually changing the set cutter level in time and observing the control system’s response to this. Please, explain this in the paper, or correct me if I’m wrong in my observation.

 

Response 11: Thank you for your valuable suggestion. The setting value for the height of the cutting blade above the ground is determined by the type of leafy vegetable. When harvesting the same type of leafy vegetable, the setting value for the height of the cutting blade above the ground remains unchanged. All simulations and measurements were conducted under different realistic working conditions. Taking the steady-state transition time as the evaluation index to analyze the stability, accuracy, and rapidity of the automatic control system of the cutter height from the ground under the incremental PID control strategy.

 

Point 12: Crossing the ditch: a narrow strip of lower ground was in front of the harvester which led the sensor to believe that the cutter was too high, therefore it should be lowered.

Another interpretation: the wheels entered the ditch which lowered the cutter and it should be lifted.

As I understand, the first case is what you intended. Please clarify this in the paper.

 

Response 12: Thank you for your valuable suggestion. The first case is what my intended. Crossing the ditch: a narrow strip of lower ground was in front of the harvester which led the sensor to believe that the cutter was too high, therefore it should be lowered.

 

Point 13: In both simulation and experiment it should be clearly stated what the reaction should be, and what actually happened. Which direction of movement is represented as positive, which one as negative? Did the system actually lower or lift the cutter? Please be explicit about these elements in the presentation of the results.

 

Response 13: Thank you for your valuable suggestion. The clockwise direction of motion of a stepper motor is positive. The counterclockwise direction of motion of a stepper motor is negative. Due to the connection between the cutting blade and the conveying platform, the system actually lowers or raises the cutting blade by driving the ball screw device to lower or raise the conveying platform through the rotation of the stepper motor.

 

Point 14: In Figure 9, d) and e) the reference (set values) and actual outputs never get equal (the set value is never reached?). Why is that? Please comment on this.

 

Response 14: Thank you for your valuable suggestion. I have consulted the literature on automatic control theory, according to the relevant knowledge of the principle of automatic control, when the actual value of cutter height above the ground enters into the ±2% range of the set value again and no longer exceeds the time for steady-state transition. The ±2% range of the set value is called steady state. As long as the actual value of cutter height above the ground is always in the ±2% range of the set value, the system is always in steady state.

 

Point 15: Figure 10 e) and Figure 14 should show the exact same thing. Why is in Figure 14 (the real measurement) only one motion (in the negative direction), and not two motions in both directions as in Figure 10 e)? If I understand it correctly, the upward slope came about, the cutter should go up, then down (when the whole machine is driven on the slope). In that sense, why is there only the downward motion in Figure 14 (if I’m not mistaken)?

 

Response 15: Thank you for your valuable suggestion. The simulation in Figure 10(e) simulates the harvester suddenly crossing a ditch at 1s and suddenly climbing a slope at 3s, where Figure 9 has simulated the harvester suddenly crossing a ditch at 1s and the simulation in Figure 10 focuses on the harvester suddenly climbing a slope at 3s. Figure 14 shows only the harvester suddenly climbing a slope during the field verification test and does not include the harvester suddenly crossing a ditch. Figure 13 shows the harvester suddenly crossing a ditch during the field test.

 

Point 16: I’m having a hard time finding the connection between the suggested model (Figure 6) and the given equations (1 to 7). Equations (1) – (5) seem correct to me. (7) is simple enough to understand and also seems correct. However, it is not the case with equation (6), where does it come from? It might be a good idea to remove from the paper all the equations which are not used in any meaningful way. Please comment on this.

 

Response 16: Thank you for your valuable suggestion. I apologize that the equation (6) which is not used in any meaningful way. I have deleted the equation (6).

 

Point 17: You state your assumptions about the model (line 203):

1) the effect of stator current on the motor was not taken into account

Please explain what you mean by that. The torque of the stepper depends on the stator current (Ia and Ib) and it seems to me that this has been taken into account (by equation 4). You also have a current PID in the automatic control system (Figure 8), which means that stator current is an important part of the model and control system, otherwise it wouldn’t make sense? Please comment on that.

The other assumptions (2 – 4) seem to be in order to me.

 

Response 17: Thank you for your valuable suggestion. I apologize that the assumption 1) is not reasonable. I have deleted the assumption 1).

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

 

I have the following comments:

1) The introduction section is sufficient.

2) The resolution of all figures must be improved (especially the Simulink based ones).

3) The flowchart given in Figure 5 must be explained in the text.

4) The related references may be provided before the equations.

5) The reported works discussing different PID control strategies such as “https://doi.org/10.1177/01423312211019633” and https://doi.org/10.1007/s12530-021-09402-4 must be discussed in the introduction.

6) Check the Simulink model in Figure 8 and correct the connection errors.

I will be happy to re-evaluate the paper after revision. Good luck.

Minor editing of English language required

Author Response

Response to Reviewer 3 Comments

Point 1: The introduction section is sufficient.

 

Response 1: Thank you very much for taking time out of your busy schedule to make invaluable suggestions to me. Thank you for your recognition and support of our work. "Agriculture" magazine is a very good journal. It is my honor to have my manuscript accepted by "Agriculture", and I also hope that my manuscript can be accepted by it. Please also kindly contact me if you have any suggestions during the review of my manuscript. Thanks again for the suggestion you gave me during your busy schedule.

 

Point 2: The resolution of all figures must be improved (especially the Simulink based ones).

 

Response 2: Thank you for your valuable suggestion. I apologize that all figures in this manuscript are too low resolution. The modified figures are shown in Figure 1(a) to Figure 22(a).

Figure 1(a). SLIDE FW leafy vegetable harvester.

Figure 2(a). 4UGS2 type double row sweet potato harvester.

Figure 3(a). Sketch of the structure of the 4UM-120D electric leafy vegetable harvester.

Figure 4(a). Automatic adjustment system of cutter height from the ground.

Figure 5(a). Flow chart of the automatic adjustment program of the cutter height off the ground.

Figure 6(a). Model of cutter height adjustment system from the ground.

Figure 7(a). Position-based PID control schematic.

Figure 8(a). Incremental PID-based model for automatic control system of cutter height off the ground.

Figure 9(a). The simulation results of stepper motor voltage, current, electromagnetic torque, rotation speed and rotation angle with sudden over-groove in smooth condition under incremental PID control strategy for automatic control system of cutter height off the ground.

Figure 10(a). The simulation results of stepper motor rotation speed(mm/s) with sudden over-groove in smooth condition under incremental PID control strategy for automatic control system of cutter height off the ground when the pitch of ball screw device is 20mm.

Figure 11(a). The simulation results of stepper motor rotation distance(mm) with sudden over-groove in smooth condition under incremental PID control strategy for automatic control system of cutter height off the ground when the pitch of ball screw device is 20mm.

Figure 12(a). The simulation results of stepper motor setting rotation speed and actual rotation speed with sudden over-groove in smooth condition under incremental PID control strategy for automatic control system of cutter height off the ground.

Figure 13(a). The simulation results of stepper motor setting rotation angle and actual rotation angle with sudden over-groove in smooth condition under incremental PID control strategy for automatic control system of cutter height off the ground.

Figure 14(a). The simulation results of stepper motor voltage, current, electromagnetic torque, rotation speed and rotation angle with abrupt climbing in smooth condition based on incremental PID control strategy for automatic control system of cutter height off the ground.

Figure 15(a). The simulation results of stepper motor rotation speed(mm/s) with abrupt climbing in smooth condition based on incremental PID control strategy for automatic control system of cutter height off the ground when the pitch of ball screw device is 20mm.

Figure 16(a). The simulation results of stepper motor rotation distance(mm) with abrupt climbing in smooth condition based on incremental PID control strategy for automatic control system of cutter height off the ground when the pitch of ball screw device is 20mm.

Figure 17(a). The simulation results of stepper motor setting rotation speed and actual rotation speed with abrupt climbing in smooth condition based on incremental PID control strategy for automatic control system of cutter height off the ground.

Figure 18(a). The simulation results of stepper motor setting rotation angle and actual rotation angle with abrupt climbing in smooth condition based on incremental PID control strategy for automatic control system of cutter height off the ground.

Figure 19(a). Incremental PID-based automatic control system device for cutter height off the ground.

Figure 20(a). 4UM-120D electric leafy vegetable harvester field operation map.

Figure 21(a). Response effect of incremental PID-based automatic control system of cutter height off the ground when the harvester suddenly crosses a ditch.

Figure 22(a). Response effect of incremental PID-based automatic control system of cutter height off the ground when the harvester suddenly climbs a slope.

 

Point 3: The flowchart given in Figure 5 must be explained in the text.

 

Response 3: Thank you for your valuable suggestion. Figure 5 depicts the system program flow chart, which mostly finished the functions of measuring, displaying, and controlling the cutter height above the ground. Set the zero limit proximity switch as the first reference point, enter the setting value for green vegetable stubble height into the touch screen, and then start the first parameter search. The slider in the ball screw device would not move at this time if the distance-measuring photoelectric sensor determined that the height of the cutting blade from the ground was always within ±2% of the set leafy vegetable stubble height, i.e., the leafy vegetable harvester did not have the phenomenon of ditch crossing or slope climbing. When the photoelectric sensor determined that the height of the cutting blade from the ground was less than 98% of the predetermined height of the leafy vegetable stubble, the leafy vegetable harvester entered the climbing condition, and the PLC calculated the difference between the current value of the cutting blade from the ground and the predetermined value to obtain the deviation and calculated the number and frequency of pulse signals that the stepper motor driver should receive through the control strategy. Thus, the stepper motor was rotated to drive the lead screw device to adjust the height of the cutter from the ground at a specific speed. When the height of the cutter from the ground was within ±2% of the preset stubble height of leafy vegetables, the stepper motor stopped rotating. Additionally, when the stepper motor was rotating to adjust the height of the cutter from the ground, if the left limit switch was on, the stepper motor also stopped rotating to prevent the slide block from hitting the stepper motor and causing motor damage. Thus, the automatic control of the height of the cutter from the ground when climbing was realized. The leafy vegetable harvester was in the situation of a ditch crossing when the photoelectric sensor determined that the height of the cutting blade from the ground was greater than 102% of the predetermined height of the leafy vegetable stubble. The PLC determined the deviation by calculating the difference between the cutting blade's current value and its set value from the ground. It then determined how many and how frequently pulse signals the stepper motor driver should receive through the control strategy. Consequently, the stepper motor was driven to move the slider at the appropriate speed to change the height of the cutter from the ground. When the height of the cutter from the ground was within ±2% of the preset stubble height of leafy vegetables, the stepper motor stopped rotating. Additionally, when the stepper motor was rotating to adjust the height of the cutter from the ground, if the right limit switch was on, the stepper motor also stopped rotating to prevent the cutter from being damaged by touching the ground due to the low height of the cutter from the ground. Thus, the automatic control of the height of the cutter from the ground when crossing a ditch was realized.

 

Point 4: The related references may be provided before the equations.

 

Response 4: Thank you very much for taking time out of your busy schedule to make invaluable suggestions to me. I apologize that the related references are not provided before the equations. The added references before the equations and the revised contents are shown below.

To vary the cutter height above the ground on the 4UM-120D electric leaf vegetable harvester, a two-phase hybrid stepper motor was used. This motor's rotation angle and speed could be changed by altering the quantity and frequency of pulse signals received by the stepper motor driver. As a result, the two-phase hybrid stepper motor mathematical model was developed [1]. Consider as an example a two-phase permanent magnet hybrid stepper motor [2] and assume that: 1) the effect of stator current on the motor was not taken into account; 2) hysteresis and eddy current effects were not taken into consideration; 3) only the average component and fundamental component of air gap permeability was taken into consideration; and 4) The mutual inductance between two phase windings was ignored [3-5]. Equation (1) depicted the voltage balance equation of the phase a winding of the two-phase hybrid stepper motor. Equation (2) depicted the equivalent circuit expression of the phase a winding. Equation (3) depicted the phase of a winding's back electromotive force . Equation (4) depicted the electromagnetic torque of the two-phase hybrid stepper motor.

		（1）
		（2）
		（3）
		（4）

Where, - Winding voltage of motor stator phase a(); - Resistance of phase a winding of motor stator(); - Phase a winding current of motor stator(); - Phase b winding current of motor stator(); - Self-induction(); - Mechanical position angle(); - Back electromotive force of phase a winding of motor stator(); - Number of magnetic pole teeth; - Maximum magnetic flux of the motor(Wb); - Electromagnetic torque(); - Detent torque().

The two-phase hybrid stepper motor's mechanical dynamics equation was displayed in equation (5).

（5）

Where, - Total rotational inertia of motor body and load(); - Motor angular speed(); - Viscous friction coefficient of motor body and load(); - Load torque().

The number and frequency of pulse signals received by the stepper motor through the driver could adjust the rotation angle and speed of the motor. Take the two-phase permanent magnet hybrid stepper motor as an example, without considering the load, the transfer function was:

（6）

Where, - Transfer function of two-phase hybrid stepping motor; -Actual value of motor rotation angle(); - Set value of motor rotation angle(); - Back potential coefficient(); - Current gain; - Rotating speed gain; - Resistance of motor stator winding().

References

1. Zhou Yifei. Simulation of stepper motor control system based on Simulink[D]. Southwest Jiaotong University, 2014.
2. Wang Lei, Lv Donghao. Optimal design and simulation of acceleration and deceleration curves of stepper motors[J]. Automation Applications, 2021(01): 21-24.
3. Xu Wenqiang, Yan Jianhong. Derivation of transfer function model for two-phase hybrid stepper motor[J]. Space Electronics, 2011, 8(03): 50-53.
4. Yang Lin, Jia Yunlong, Li Yang, et al. Modeling and simulation of short arc removal rivet system[J]. Electrical Processing and Tooling, 2022, No.366(S1): 24-29.
5. Qi Zhenya, Qin Qianqian, Wang Liying, et al. Simulation study of constant current subdivision drive control for two-phase hybrid stepper motor[J]. Microtechnology, 2022, 50(09): 48-52.

 

Point 5: The reported works discussing different PID control strategies such as “https://doi.org/10.1177/01423312211019633” and https://doi.org/10.1007/s12530-021-09402-4 must be discussed in the introduction.

 

Response 5: Thank you for your valuable suggestion. The added references and the revised contents are shown below.

Yang Long implemented closed-loop pressure control by incorporating the position-based PID control algorithm into the pressure control architecture. It was confirmed by MATLAB simulation that the design accomplished the desired control goal, however its control effect is only relevant to pressure control situations with lower precision requirements [1]. In order to ensure safe and reliable driving of autonomous vehicles along a predetermined course, Tan Baocheng et al. suggested a new incremental PID control method by enhancing and optimizing the conventional incremental PID control algorithm. Using the new incremental PID control technique, experimental results demonstrate that unmanned vehicle path tracking rise time and adjustment time are lowered, response speed is increased, overshoot is decreased, and the vehicle achieves quick and stable path tracking [2]. The method of employing an incremental PID control algorithm to steer an intelligent vehicle is described by Xiao Wenjian et al. The test demonstrates that the adoption of an incremental PID control method improves the stability and speed of the cart as well as the speed and response of the intelligent vehicle servo [3].

References

1. Yang Long. Design and MATLAB simulation of pressure control based on positional PID algorithm[J]. Electronic Technology and Software Engineering, 2018, No.146(24): 27.
2. Tan Baocheng, Wang Bin. Incremental PID control for unmanned vehicle path tracking[J]. Journal of Xi'an University of Technology, 2016, 36(12): 996-1001.
3. Xiao Wenjian, Li Yongke. Intelligent vehicle design based on incremental PID control algorithm[J]. Information Technology, 2012, 36(10): 125-127.

 

Point 6: Check the Simulink model in Figure 8 and correct the connection errors.

 

Response 6: Thank you for your valuable suggestion. I apologize that there are connection errors in the Simulink model in Figure 8. The modified Simulink model is shown in Figure 8(a).

Figure 8(a). Incremental PID-based model for automatic control system of cutter height off the ground.

Please see the attachment.

Author Response File: Author Response.pdf